Determining percentages is an important mathematical skill used in many real-world situations.
In this article, we will explore the question “220 is what percent of 400?” step-by-step and discuss various methods to find the percentage.
Utilizing the “X is What Percent of Y Calculator”,we can compute that 220 is 55% of 400.
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Step-by-Step Solution: 220 is What Percent of 400?
Now that we know we want to find 220 is what percent of 400? , let’s look at two different step-by-step methods we can use to solve this percentage problem. Each approach arrives at the same solution, but understanding different ways to think through the math builds flexibility and deeper learning.
Method 1: Convert Ratio to Percentage
Fractions consist of a numerator and denominator. Fractions consist of a numerator and denominator. The numerator represents the number of pieces being considered, while the denominator is the total number of pieces that make up the whole.
“Percent” means “per hundred”. So percent is another way to express a fraction where the denominator is always 100.
For example, the percentage 50% indicates we have 50 out of a total of 100 pieces. 50% can be rewritten as the fraction 50/100, since we have 50 parts out of 100 total parts.
In summary, to convert a fraction to a percentage, we multiply the numerator and denominator by the same value so that the denominator becomes 100. Once we have a fraction with a denominator of 100, the numerator gives us the percentage amount. This allows any fraction to be converted to an equivalent percentage based on the concept of “out of 100”.
Let’s apply this understanding to calculate “220 is what percent of 400?”.
Step1: Write the Ratio as a Fraction
First, we can express “220 is what percent of 400?” as the fraction 220/400.
220 of 400 can be written as: 220 400
Step 2: Find the Number to Multiply to Get a Denominator of 100
We want the denominator to be 100, so need to multiply by a number that makes 400 into 100
To find this number, divide 100 by 400:
100 400 = 0.25
Step 3: Multiply the Fraction by the Number from Step 2
Multiply both the numerator and denominator by 0.25:
220400 x 0.250.25
= 220 x 0.25400 x 0.25
= 55100
Step 4: The Numerator is Now the Percentage
Since our new denominator is 100, the numerator 55 represents the percentage
This step-by-step method of converting the ratio 220 : 400 to a fraction and then a percentage with a denominator of 100 allows us to calculate that 220 is 55% of 400.
Method 2: Converting Fractions to Decimals and Percents
You can also use division to convert a fraction to a decimal and then to a percentage.
Step 1: Write the Fraction
Start with the original fraction:
220 of 400 can be written as: 220 400
Step 2: Divide the Numerator by the Denominator
Use long division to divide the numerator by the denominator:
220 400 = 0.55
Step 3: Multiply the Decimal by 100
To convert the decimal to a percentage, multiply it by 100:
0.55 x 100 = 55%
Therefore, by dividing 220/400 to 0.55 and then multiplying by 100, the result is 55%
Following this process carefully of dividing the fraction, multiplying the decimal by 100, and interpreting the result as a percentage provides us another method to find that 220 is 55% of 400.
Comparing the Two Methods
Let’s summarize the two methods we used to find the percentage “220 is what percent of 400?”:
Method | Description | Steps |
---|---|---|
Convert Ratio to Percentage | Converts the ratio to a fraction, then multiplies to make the denominator 100 | 1. Write ratio as fraction 2. Multiply to make denominator 100 3. Numerator is the percentage |
Convert Fraction to Decimal and Percentage | Divides the fraction to a decimal, then multiplies the decimal by 100 | 1. Write the fraction 2. Divide numerator by denominator 3. Multiply decimal by 100 4. Result is the percentage |
The ratio to percentage method directly converts the ratio 220 : 400 to an equivalent percentage fraction. The fraction to decimal method indirectly converts the fraction 220/400 to a decimal and then a percentage.
p>Both methods follow a clear step-by-step procedure to arrive at the same result that 220 is 55% of 400. Understanding multiple approaches builds flexibility in thinking through percentage problems.
Standard Percentage of 400 Calculation Examples
Now that we have calculated that 220 is 55% of 400, let’s explore what 5%, 10%, up to 95% of 400 would be.
20 is 5% of 400
40 is 10% of 400
60 is 15% of 400
80 is 20% of 400
100 is 25% of 400
120 is 30% of 400
140 is 35% of 400
160 is 40% of 400
180 is 45% of 400
200 is 50% of 400
220 is 55% of 400
240 is 60% of 400
260 is 65% of 400
280 is 70% of 400
300 is 75% of 400
320 is 80% of 400
340 is 85% of 400
360 is 90% of 400
380 is 95% of 400
400 is 100% of 400
Conclusion
Finding percentages is an essential mathematical skill used in daily life for calculations of discounts, taxes, tips, interest rates, test scores, and more. In this article, we explored the specific question “220 is what percent of 400?” and discussed two methods to solve it – converting a ratio to a percentage and converting a fraction to a decimal and percentage. Both methods carefully followed arrive at the solution that 220 is 55% of 400.
We also looked at calculating a range of standard percentages from 5% to 95% of the total number 400. Practicing these types of percentage calculations helps improve mathematical proficiency and comfort applying different techniques.